Bifurcation and stability of stationary solutions of the Fitz-Hugh-Nagumo equations

DOI10.1016/0022-0396(86)90062-8zbMath0605.58031OpenAlexW1988734580MaRDI QIDQ1083743

J. A. Smoller, Charles C. Conley

Publication date: 1986

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2027.42/26127

zbMATH Keywords

stabilitybifurcationMorse indexConley indexFitz-Hugh-Nagumo equations

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Applications of dynamical systems (37N99) Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (6)

Existence of semi-nodal solution for a class of Fitzhugh-Nagumo type system ⋮ Charles C. Conley, 1933–1984 ⋮ Hopf bifurcation in a reaction-diffusion system governed by the Fitz- Hugh-Nagumo equations ⋮ Lyapunov functionals and stability for FitzHugh-Nagumo systems ⋮ Large patterns of elliptic systems in infinite cylinders ⋮ Eliminating synchronization of coupled neurons adaptively by using feedback coupling with heterogeneous delays

Cites Work

• Global bifurcation of steady-state solutions
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Qualitative theory of the Fitz Hugh-Nagumo equations
• Semilinear Parabolic Problems Define Semiflows on C k Spaces
• Non-degenerate solutions of boundary-value problems
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